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| United States Patent |
5,538,243
|
|
Yamamoto
, et al.
|
July 23, 1996
|
Tennis racket frame
Abstract
A tennis racket frame comprising a string-installing portion (10), T-shaped
in cross section, formed along the entire periphery of a ball-hitting
surface thereof. The string-installing portion (10) comprises a projection
(20) formed toward the ball-hitting surface in which strings are installed
and a base (21) perpendicular to the projection (20). A plurality of gut
holes (25) are formed on the projection (20) such that each of the gut
holes (25) penetrates through the center thereof. A plurality of gut holes
(24) is formed on the bottom surface of a concave (23) of the base (21)
such that each of the gut holes (24) penetrates through the center of the
base (21).
| Inventors:
|
Yamamoto; Ken (Akashi, JP);
Nakamura; Teruo (Yokohama, JP)
|
| Assignee:
|
Sumitomo Rubber Industries, Ltd. (Hyogo-Ken, JP)
|
| Appl. No.:
|
209245 |
| Filed:
|
March 14, 1994 |
Foreign Application Priority Data
| Current U.S. Class: |
473/537 |
| Intern'l Class: |
A63B 049/14 |
| Field of Search: |
273/73 C,73 G,73 R,73 D,73 H,730,DIG. 1
|
References Cited
U.S. Patent Documents
| 3647211 | Mar., 1972 | Doessel et al. | 273/73.
|
| 5009422 | Apr., 1991 | Soong | 273/73.
|
| 5102132 | Apr., 1992 | Chen | 273/73.
|
Primary Examiner: Millin; Vincent
Assistant Examiner: Anderson; Charles W.
Attorney, Agent or Firm: Birch, Stewart, Kolasch & Birch, LLP
Claims
What is claimed is:
1. A tennis racket frame comprising a ball hitting surface, a
string-installing portion formed along an entire periphery of the
ball-hitting surface thereof, a throat portion and a grip portion,
wherein said string-installing portion has a T-shaped configuration in
cross section in which the base of the T defines a projection which
extends toward the ball-hitting surface in which strings are installed and
the top of the T defines a base which is perpendicular to the projection.
said projection and said base being formed symmetrically with respect to a
center line passing through a center of the projection wherein the
relationship between a width (b1) of the projection and a width (B) of the
string installing portion is defined by the following formula (A) and the
relationship between a thickness (h1) of the projection and thickness (h)
of the base is defined by the following formula (B):
(A) 3 mm.ltoreq.b1.ltoreq.0.8B
(B) 3 mm.ltoreq.h1.ltoreq.0.75h,
said string-installing portion having a plurality of gut holes formed
therein which pass through the center of said projection and through the
center of the base.
2. The tennis racket frame as defined in claim 1, wherein said
string-installing portion is hollow and has a concave portion formed on an
outer surface of said base, said concave portion being provided with a
grommet.
3. The tennis racket frame as defined in claim 1, wherein the gut holes are
formed at regular intervals and through a center line passing through the
center of the projection.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a tennis racket frame and more
particularly, to a tennis racket having a favorable repulsion performance
and ball control performance and giving a soft ball-hitting feeling to a
player by improving the cross sectional configuration of a
string-installing portion of the frame thereof.
2. Description of the Related Art
Research has been made to improve the performance of the tennis racket and
as a result, tennis rackets in various configurations have been proposed.
The configurations of the tennis rackets developed recently are classified
into the following three types:
1. Mid (standard) size racket;
2. Rackets having a large ball-hitting surface, namely, the so-called large
racket; and
3. Rackets having a large vertical sectional area of a string-installing
section of the racket frame, namely the so-called thick racket.
A tennis racket is required to have a favorable repulsion performance and
ball control performance and provide a soft ball-hitting feeling to a
player. The main factor for determining these performances is the spring
characteristics.
The spring characteristics are classified into the following four types as
shown in FIGS. 15A, 15B, and 15C in consideration of the construction of
the racket.
(1) Spring shown by (A) of FIG. 15 generated by the deformation of strings
1[.];
(2) Spring shown by (B) of FIG. 15 generated by the deformation of a
supporting portion (string-installing portion) 2 for supporting the
strings 1;
(3) Spring shown by (C) of FIG. 15 generated by the in-plane deformation of
a racket frame 3; and
(4) Spring shown by (D) of FIG. 15 generated by the out-of-plane
deformation of the racket frame 3.
It is considered that the above four springs are connected in series with
each other and hence a most deformable spring determines the
characteristic of the racket.
Observing the deformation of the mid (standard) size racket which occurs
when a tennis ball collides with the ball-hitting surface thereof, the
racket frame 3 is deformed like a spoon as shown in FIG. 15C. The spring
(D) generated by the out-of-plane deformation of the racket frame 3 is the
main factor for determining the characteristic of the racket.
Because the ball-hitting area of the mid size racket is smaller than that
of the large racket, the in-plane rigidity of the former is higher than
that of the latter and thus, the stability of ball-hitting surface of the
former is more favorable than that of the latter and hence, ball control
performance of the former is higher than that of the latter.
Because the thickness (h) of the string-installing portion 2 is smaller
than that of the thick racket, the out-of-plane rigidity of the former is
low and thus, the mid size racket is flexible and gives a soft feeling to
the player in hitting a tennis ball.
As described above, the mid size racket has a favorable ball control
performance and gives a soft feeling to the player in hitting the tennis
ball, but the spring main factor for determining the characteristic
thereof is generated due to the spring (D) caused by the out-of-plane
deformation of the racket frame 3. The spring (D) does not greatly
contribute to the improvement of the repulsion performance of the racket.
The large racket and the thick racket have been developed to improve the
repulsion performance of the racket.
In the large racket having a large ball-hitting area, the spring (A)
generated by the deformation of the strings 1 is the main factor for
determining the characteristic thereof and thus the large racket has a
favorable repulsion performance.
In the thick racket in which the thickness (h) of the string-installing
portion 2 is great, the main factors for determining the characteristic
thereof are the spring (A) generated by the deformation of the strings 1
and the spring (B) generated by the deformation of string-installing
portion 2. In particular, curved peripheral surfaces of the
string-installing portion 2 are deformed and thus a strong spring
generated due to the return of the deformation of the curved peripheral
surfaces displays a higher repulsion performance than the large racket.
The string-installing portion 2 of the conventional tennis racket frame has
an approximately rectangular, sectional configuration as shown in FIG.
16A; an approximately, octagonal sectional configuration as shown in FIG.
16B; or an approximately elliptical, sectional configuration as shown in
FIG. 16C. The frame has, on the center of the outer side of the
string-installing portion 2, a concave portion 2a into which a grommet
used to install a string thereon is inserted; and has gut holes 2b and 2c
on the center of the bottom surface of the concave portion 2a and the
inner side of the string-installing portion 2 opposed to the center of the
bottom surface of the concave portion 2a, respectively.
The thickness (h) of the mid size racket and that of the thick racket are
approximately 20 mm and 30 mm at the largest portion thereof,
respectively.
The ball-hitting area of the mid size racket and that of the large racket
are approximately 93 to 95 square inches and 105 to 108 square inches,
respectively.
As described above, the large racket and the thick racket have a higher
repulsion performance than the mid size racket, respectively, whereas they
have a lower ball control performance than the mid size racket and give a
less soft ball-hitting feeling to the player than the mid size racket for
the reason which is described below.
That is, because the large racket has a larger ball-hitting area than the
mid size racket, the in-plane rigidity of the ball-hitting surface of the
large racket is lower than that of the mid size racket and thus the
deformation amount of the in-plane deformation of the former is greater
than that of the latter. Thus, the stability degree of the ball-hitting
surface of the large racket is inferior and thus the ball control
performance thereof is unfavorable.
In the thick racket, the deformation of the spring (B) generated by the
deformation of the string-installing portion 2 is restored in a shorter
time period than the other springs (A), (C) and (D). Thus, the period of
time in which the thick racket and the ball are in contact with each other
is short and thus the ball control performance thereof is unfavorable.
In addition, because the thickness (h) of the thick racket is great, the
thick racket does not generate the out-of-plane deformation, thus giving a
hard ball-hitting feeling to the player when the player hits the ball with
the thick racket. Impacts generated in ball hitting are transmitted to the
arm of the player. Hence, when the player continues to use the thick
racket for a long time, the player may develop a tennis elbow on the arm
or the elbow.
SUMMARY OF THE INVENTION
It is accordingly an object of the present invention to provide a tennis
racket which is superior in repulsion performance and ball control
performance and gives a soft ball-hitting feeling to a player.
In accomplishing these and other objects of the present invention, there is
provided a tennis racket comprising a string-installing portion which is
T-shaped in cross section, formed along the entire periphery of a
ball-hitting surface thereof, wherein the string-installing portion
comprises a projection formed toward the ball-hitting surface in which
strings are installed and a base perpendicular to the projection.
The string-installing portion is hollow and has a plurality of gut holes
formed on the projection such that each of the gut holes penetrates
through the center thereof and a plurality of gut holes formed on the
bottom surface of a concave portion of the base such that each of the gut
holes penetrates through the center of the base.
The projection and the base are symmetrical with respect to a center line
passing through the center of the projection. The gut holes are formed
along the center line passing through the center of the projection.
It is possible to deviate the projection and the base from each other. It
is also possible to incline the gut holes with respect to the center line
passing through the center of the projection.
A fiber reinforced resin is molded into the racket frame.
Preferably, each corner of the string-installing portion is rounded.
It is preferable to set the width b1 of the projection and the thickness h1
of the projection as follows:
3 mm.ltoreq.b1.ltoreq.0.7B, 3 mm.ltoreq.h1.ltoreq.0.75h where B is the sum
of the width of the base and the width b1 of the projection, and h is the
thickness of the base.
According to the above construction, because the string-installing portion
of the tennis racket frame is T-shaped in cross section, torsion
deformation is generated on the string-installing portion when a ball is
hit by the racket. The restoring force of the deformation imparts a
spring, which cannot be provided by the conventional tennis racket, to the
tennis racket according to the present invention. Different from the
conventional springs adopted in the conventional large or thick racket,
which acts by the sacrifice of other springs, the string-installing
portion of the present invention displays its force in harmony with the
four springs described previously. That is, the novel spring has the
following characteristic:
(1) When the string-installing portion, which is T-shaped in cross section,
is adopted in a mid size racket, the mid size racket provides repulsion
performance as favorably as the thick racket in addition to the advantage
of the mid size racket, namely, a favorable ball control performance and a
soft feeling given to a player when the player hits a tennis ball.
(2) When the string-installing portion, which is T-shaped in cross section,
is adopted in the large racket, the large racket improves the stability of
the ball-hitting surface thereof and provides a favorable ball control
performance and a soft feeling to the player when the player hits the ball
in addition to a favorable repulsion performance.
(3) When the string-installing portion, which is T-shaped in cross section,
is adopted in the thick racket, the racket provides a favorable ball
control performance and increases the period of time in which the racket
is in contact with the ball and increases ball control performance, thus
giving a soft ball-hitting feeling to the player.
The reason why the repulsion performance can be improved by the T-shaped
string-supporting portion in cross section is as follows:
That is, the repulsion performance depends on the magnitude of the
returning force of the deformation of the racket when the ball is hit and
the time period in which the ball-hitting surface and the ball are in
contact with each other. That is, the magnitude of the impulse which is
the product of the force and the time period determines the magnitude of
energy to be applied to the ball.
Curves shown by three solid lines of FIG. 17 represent the relationship
between force and the elapse of time between the time when a ball becomes
in contact with the racket and the time when the ball loses contact with
the racket in a conventional mid size racket (I), a large racket (II) and
a thin racket (III).
Referring to FIG. 17, reference symbols T.sub.1, T.sub.2, and T.sub.3
denote contact time periods, and F.sub.1, F.sub.2, and F.sub.3 denote the
maximum spring forces. The areas of portions surrounded with diagonal
lines are respective impulses. If the areas, namely, impulses are equal to
each other, the repulsion performances are equal to each other.
Accordingly, the repulsion performance can be increased by increasing
spring force and the time period of contact between the ball and the
strings.
The novel spring brought about by the torsion generated by the T-shaped
string-installing portion in cross section enhances the spring force due
to the effect of accelerating the return of the strings and in addition,
allows the time period in which the ball and strings are in contact with
each other to be long because the novel spring generates the action of
encircling the ball due to the deformation of the projection caused by
torsion.
Due to these effects, in the mid size racket, the contact period of time
T.sub.1 ' can be set to be long and a maximum spring force F.sub.1 ' can
be set to be large as shown by the chain line (I') of FIG. 18, and the
product, namely, the impulse of the contact period of time T.sub.1 ' and
the maximum spring force F.sub.1 ' can be changed to be large. Thus, it is
possible to increase the repulsion performance with the advantageous
features of the mid-size racket being maintained.
It is important that the tennis racket frame does not exceed a given
weight.
The in-plane rigidity is apt to decrease in the large racket due to its
large ball-hitting surface. If the sectional rigidity is increased by
increasing the weight of the large racket, the weight thereof exceeds the
above given weight.
In the thick racket, it is necessary to reduce the width of the
string-installing portion in cross section so that the weight of the
racket frame does not exceed the given weight. That is, the peripheral
length of the string installing portion in cross section has a limitation
because it is disadvantageous to make its weight greater than the given
weight. Therefore, if the thickness of the string-installing portion is
set to be large, supposing that the material of the racket frame is not
altered and the thickness of a wall of the string-installing portion is
not altered, it is necessary to set the width thereof to be shorter in
correspondence with the increased amount of the thickness. Therefore, in
the case of the thick racket, the width of the string-installing portion
becomes smaller in correspondence with the increased amount of thickness
and thus the in-plane rigidity is reduced similarly to the large racket.
On the contrary, because the string-installing portion, according to the
present invention, is T-shaped in cross section and the projection is
disposed on the inner side of the string-installing portion, the in-plane
rigidity can be increased without exceeding the given weight.
That is, the rigidity of the string-installing portion in cross section is
evaluated by a second moment of area (moment of inertia of area). For
example, supposing that the thickness of a rectangle shown in FIG. 19 is h
and the width thereof is b, the second moment of area is expressed as
follows:
Ix=b.times.h.sup.3 /12, Iy=b.sup.3 .times.h/12
In the above equation, Ix (second moment of area for X) is a coefficient
for determining the out-of-plane rigidity of the racket, and Iy (second
moment of area for Y) is a coefficient for determining the in-plane
rigidity thereof.
As indicated by the above equations, the second moment of area is
proportional to the cube of the distance between the rotary axis of a
sectional area and a periphery of the sectional area.
Accordingly, if the thickness (h) is set to be large without changing the
peripheral length of the rectangle in cross section, the width (b)
decreases and thus the in-plane rigidity decreases in proportion to the
cube of the width (b). If the width (b) is set to be large to increase the
out-of-plane rigidity, the thickness (h) decreases and thus the
out-of-plane rigidity is reduced in proportion to the cube of the
thickness (h). For example, if the thickness (h) is set to be twofold and
the width (b) is set to be one-half, Ix which indicates the index of the
out-of-plane rigidity becomes fourfold, whereas Iy which indicates the
index of the in-plane rigidity becomes 1/4 and thus Iy/Ix is 1/16.
Because the string-installing portion is T-shaped in cross section, the
in-plane rigidity can be increased by arbitrarily selecting the
correlation between the thickness of the string-installing portion and the
width thereof without greatly reducing the out-of-plane rigidity.
More specifically, the string-installing portion is T-shaped and a state is
generated in which the projection 20 mounted on the inner surface of the
base 21 serves as a hoop. Due to the formation of the hoop, deformation
toward the inside of the string-installing portion can be effectively
restrained and thus, the effect of the hoop, which cannot be provided by
the conventional racket frame, can be generated.
As described above, the in-plane rigidity can be designed freely, i.e., the
repulsion performance can be enhanced by increasing the ball-hitting area
without decreasing the in-plane rigidity. Accordingly, for example, a
large racket having a superior repulsion performance and a favorable
stability of the ball-hitting surface can be manufactured.
The out-of-plane rigidity of the thick racket becomes large due to its
large thickness and hence, a player has a hard ball-hitting feeling and
the time period in which the ball and the ball-hitting surface are in
contact with each other is short. Even though designing is made to
generate the out-of-plane deformation (flexibility) to some extent by
reducing flexural rigidity, on the condition that the thickness of the
string-installing portion is not reduced, the sectional width of a
rectangle or that of an ellipse is substantially reduced in the
conventional thick racket frame. Thus, it is difficult to maintain the
in-plane rigidity.
On the above point, the T-shaped string-installing portion of the present
invention restrains the in-plane deformation due to the above-described
hoop effect. Thus, it is possible to design a thick racket which is
flexible, gives a soft ball-hitting feeling, and allows the thick racket
to maintain contact with the ball for a long period of time.
In addition, the T-shaped configuration of the string-installing portion
prevents the vibration of the strings from being smoothly transmitted from
the gut holes to the entire racket frame and thus the resonance of the
racket frame with the vibration of the racket strings is avoided. The
reason for this is described in detail later. Consequently, the vibration
of the strings is restrained and the player has a favorable ball-hitting
feeling.
BRIEF DESCRIPTION OF THE DRAWINGS
These and other objects and features of the present invention will become
clear from the following description taken in conjunction with the
preferred embodiments thereof with reference to the accompanying drawings,
in which:
FIG. 1A is a front view showing a tennis racket according to a first
embodiment of the present invention;
FIG. 1B is a plan view showing the tennis racket according to the first
embodiment of the present invention;
FIG. 1C is a sectional view, showing the tennis racket according to the
first embodiment of the present invention, taken long a line III--III of
FIG. 1B;
FIG. 1D is a sectional view, showing a string-installing portion, of the
tennis racket according to a first embodiment of the present invention;
FIG. 2A is a front view showing a tennis racket according to a second
embodiment of the present invention;
FIG. 2B is a sectional view, showing a string-installing portion, of the
tennis racket according to the second embodiment of the present invention;
FIG. 3A is a sectional view showing the operation of the string-installing
portion of the tennis racket according to the present invention;
FIG. 3B is a plan view showing the operation of a principal portion of the
tennis racket according to the present invention;
FIG. 4A is a front view showing a first comparison racket;
FIG. 4B is a sectional view, showing the first comparison racket, taken
along a line 4B--4B of FIG. 4A;
FIG. 5A is a front view showing a second comparison racket;
FIG. 5B is a sectional view, showing the second comparison racket, taken
along a line 5B--5B of FIG. 5A;
FIG. 6A is a front view showing a third comparison racket;
FIG. 6B is a sectional view, showing the third comparison racket, taken
along a line 6B--6B of FIG. 6A;
FIG. 7A is a front view showing a fourth comparison racket;
FIG. 7B is a sectional view, showing the fourth comparison racket, taken
along a line 7B--7B of FIG. 7A;
FIG. 8A is a front view showing a fifth comparison racket;
FIG. 8B is a sectional view, showing the fifth comparison racket, taken
along a line 8B--8B of FIG. 8A;
FIG. 9 is a schematic view showing a method of testing repulsion
performance;
FIG. 10 is a diagram showing the relationship between restitution
coefficient and a ball-hitting area;
FIGS. 11A, 11B, and 11C are schematic views each showing a method of
testing rigidity;
FIG. 12 is a diagram showing the relationship between rigidity to plane
pressure and the ball-hitting area;
FIG. 13 is a diagram showing the relationship between rigidity to top
pressure and the ball-hitting area;
FIG. 14 is a diagram showing the relationship between rigidity to side
pressure and the ball-hitting area;
FIG. 15A, 15B, and 15C are schematic views each showing the spring effect
generated on a tennis racket;
FIG. 16A, 16B, and 16C are sectional views showing a string-installing
portion of a conventional tennis racket;
FIG. 17 is a diagram for comparing the repulsion performance of a mid
(standard) size racket, a large racket, and a thick racket with each
other;
FIG. 18 is a diagram for comparing the repulsion performance of a racket
according to the present invention and a conventional mid (standard) size
racket with each other; and
FIG. 19 is a schematic view showing a sectional rigidity of a rectangle.
DETAILED DESCRIPTION OF THE INVENTION
Before the description of the present invention proceeds, it is to be noted
that like parts are designated by like reference numerals throughout the
accompanying drawings.
A tennis racket according to a first embodiment of the present invention is
described below with reference to FIG. 1.
FIGS. 1A, 1B, 1C and 1D show a tennis racket frame according to the first
embodiment of the present invention. The tennis racket frame comprises a
string-installing portion 10, a throat portion 11, and a grip section 12.
As shown in FIGS. 1C and 1D, the string-installing portion 10 hollow and
sectionally T-shaped has a projection 20 formed on a ball-hitting side (S)
on which strings 13 are mounted.
The string-installing portion 10 is T-shaped in cross section and comprises
the projection 20 and a base 21 which are symmetrical with respect to a
center line (X) passing through the center of the projection 20. A concave
portion 23 into which a grommet is to be inserted is formed in the center
of a peripheral surface 21a of the base 21. A plurality of outer gut holes
24 spaced at regular intervals is formed at the center, of the concave 23,
through which the center line (X) passes. A plurality of inner gut holes
25 spaced at regular intervals is formed at the center, of an inner
surface 20a of the projection 20, through which the center line (X)
passes. Therefore, the outer gut hole 24 and the inner gut hole 25 are
disposed on the center line (X).
Each corner of the string-installing portion 10, namely, corners 21b and
21c of the base 21; corners 20b of the projection 20; and corners 23a of
the concave 23 is rounded at a desired curvature, respectively.
The curvature formed at the corner 20c at which the projection 20 and the
base 21 are continuous with each other has a positive curvature disposed
inside a line (shown by one-dot chain line) connecting a point P1 and a
point P2 with each other. The point P1 is b1/4 distant from the corner
20b. The point P2 is (h-h1)/8 distant from the corner 21b. The reference
symbols (b1) and (h1) denote the width and thickness of the projection 20
and (h) is the thickness of the base 21.
It is preferable to set the thickness (h) of the base 21, the thickness
(h1) of the projection 20, the width (b1) of the projection 20, and the
width (B) of the string-installing portion 10, namely, the sum of the
width (b) of the base 21 and the width (b1) of the projection 20 as
follows:
3 mm.ltoreq.b1.ltoreq.0.7B, 3 mm.ltoreq.h1.ltoreq.0.75h
Table 1 shows the dimension of each portion of the tennis racket according
to the first embodiment, the second moment of area Ix indicating the index
of the out-of-plane rigidity of the string-installing portion 10, the
second moment of area Iy indicating the index of the in-plane rigidity of
the string-installing portion 10. Reference symbol (B) shown in Table 1
indicates the whole width of the string-installing portion 10. Although
not shown in Table 1, the width (b) of the base 21 is 6 mm, a thickness
(m) of a wall of the string-installing portion is 1 mm, and the whole
length (L) of the racket frame is 685 mm.
In the first embodiment, the thickness of the top side of the
string-installing portion 10 is equal to that of the end of the throat
portion 11 on the grip side thereof.
TABLE 1
______________________________________
Sectional ball
configuration hitting out-of-plane
in-plane
(side) [mm] area rigidity rididity
h B h1 b1 [in.sup.2 ]
Ix (mm.sup.4)
Iy (mm.sup.4)
______________________________________
E1 21 12 8.5 6 100 2300 1000
E2 21 17 8.5 10 100 2300 1300
C1 20 12 . . .
. . .
93 1900 1000
C2 21 12 . . .
. . .
95 2300 1300
C3 21 12 . . .
. . .
105 2300 1300
C4 30 13.5 . . .
. . .
97 5400 1500
C5 30 12.5 . . .
. . .
108 5400 1500
______________________________________
In the above, the sectional configuration indicate that of the
string-installing portion positioned at a side of racket frame encircling
the ball-hitting surface, E1 and E2 indicate tennis racket according to
first embodiment and second embodiment, respectively; C1 through C5
indicate first comparison tennis racket through fifth comparison tennis
racket, respectively.
FIGS. 2A and 2B show a tennis racket according to a second embodiment. The
string-installing portion 10 are gradually thickened from the end of the
throat portion 11 on the grip side toward the top side 10-1 of the
string-installing portion 10. That is, the thickness (h) of base 21 of the
string-installing portion 10 is 21 mm at the top side 10-1 thereof and
that of the throat portion 11 is 19 mm at the end thereof on the grip
side.
In the string-installing portion 10 of T-shaped cross section, the
peripheral surface 21a of the base 21 thereof are inclined to form tapered
portions 26 and 27 on both sides of the concave 23.
Table 1 shows the dimension of each portion of the tennis racket according
to the second embodiment, the second moment of area Ix indicating the
index of the out-of-plane rigidity of the string-installing portion 10,
the second moment of area Iy indicating the index of the in-plane rigidity
of the string-installing portion 10. The thickness (m) of the wall of the
string-installing portion is equal to that of the racket frame according
to the first embodiment, namely, 1 mm. The whole length (L) of the racket
frame also is equal to that of the racket frame according to the first
embodiment.
The following operations are performed by the racket frame comprising the
string-installing portion 10 of T-shaped cross section and the projection
20 projecting toward the ball-hitting surface:
Firstly, the tennis racket has a favorable repulsion performance because of
the spring generated by torsion deformation of the string-installing
portion 10.
That is, as shown in FIG. 3A, the tensile force of each string 13 is
resolved into an in-plane component and an out-of-plane component due to
the deformation of the string 13 caused by ball hitting, and the two
components are transmitted to each gut hole 25 of the string-installing
portion 10.
In the string-installing portion 10 of T-shaped cross section, torsion as
shown by an arrow of FIG. 3 is generated due to the out-of-plane component
applied to the leading end of the projection 20 positioned at the
periphery of the ball-hitting surface. The spring produced by the return
of the deformation (torsion) is applied to the tennis ball as a novel
spring which is not generated by the conventional tennis racket. The
torsion is transmitted all around the ball-hitting surface of the racket
frame as shown by the double arrows of FIG. 3B. The torsion is supported
by the throat portion 11 and transmitted to the grip portion 12.
The racket according to the present invention has repulsion performance
superior to the conventional racket due to the novel spring action
generated by the torsion.
The second operation of the racket frame according to the present invention
is described below. It is difficult to make the designing of the in-plane
rigidity and the out-of-plane rigidity freely, whereas according to the
present invention, it is possible to do so by selecting an appropriate
thickness and width of the string-installing portion 10, because the
string-installing portion 10 is T-shaped in cross section.
That is, as described above, because there is a limitation in the weight of
the racket frame, the peripheral length of the string-installing portion
10 in the sectional configuration thereof has a limitation in
consideration of the weight of the racket frame. If the limitation of the
weight is to be satisfied, there is a limitation in the peripheral length
of the string-installing portion 10. If the thickness (h) of the
string-installing portion 10 is set to be large, it is necessary to reduce
the width (B) thereof in correspondence with the increased amount of the
thickness (h).
The rigidity of the racket is expressed by the second moment of area as
follows:
Ix=b.times.h.sup.3 /12, Iy=b.sup.3 .times.h/12
where Ix is a coefficient for determining the out-of-plane rigidity of the
racket, and Iy is a coefficient for determining the in-plane rigidity
thereof, as described previously.
Because the string-installing portion 10 is T-shaped in cross section, the
value of the in-plane rigidity can be allowed to be within a required
numerical range by appropriately selecting the thickness (h) of the base
21, the thickness h1 of the projection 20, the width b1 of the projection
20, and the width (B) of the string-installing portion 10. Thus, even
though the ball-hitting area is set to be large, it is possible to design
a high second moment of area Iy indicating the index of the in-plane
rigidity, which allows even the large racket to have a high ball control
performance.
Further, it is possible to enlarge the thickness (h) without increasing the
second moment of area Ix indicating the out-of-plane rigidity by selecting
the thickness (h) of the base 21, the thickness h1 of the projection 20,
the width b1 of the projection 20, and the width (B) of the
string-installing section 10.
That is, in designing the thick racket or a racket thinner than the thick
racket and thicker than the mid size racket, it is possible to apply a
spring generated by the spoon-shaped bending deformation to the spring
generated by the conventional "thick racket" due to a decrease of the
out-of-plane rigidity for the thickness (h).
As described above, according to the present invention, because the
in-plane rigidity can be made to be high, even though the ball-hitting
surface is set to be large, even the large racket has an improved ball
control performance. Further, even a thick racket has a favorable ball
control performance and gives the player a soft ball-hitting feeling by
making the out-of-plane rigidity smaller for the thickness of the
string-installing portion.
The third operation of the racket frame according to the present invention
is a restraint of the vibration generated by strings 13.
Both vertical and horizontal strings 13 vibrate similarly to a vibration of
a film after the ball collides with the strings 13 and becomes out of
contact therewith. Thus, the vibration mode of the strings 13 changes
rapidly from a primary mode to a high frequency mode and the vibrations of
the strings 13 attenuate. The vibrations of the strings 13 are transmitted
to the inner periphery of the string-installing portion 10 with the
strings 13 being in contact with the peripheries of the inner gut holes 25
disposed in the inner periphery of the string-installing portion 10.
Vibration waves thus generated are transmitted to the grip portion 12 via
the throat portion 11.
In the conventional racket, elastic waves are generated on the inner
periphery of the string-installing portion due to the vibrations of the
strings transmitted from the gut holes. Then the elastic wave is
transmitted to the entire frame.
On the other hand, because the string-installing portion 10 according to
the present invention is T-shaped in cross section, elastic waves
generated by the vibrations of the strings 13 transmitted from the gut
holes 24 and 25 are curved and thus not transmitted smoothly to the entire
frame. That is, the vibrations of the strings 13 are transmitted to the
grip portion 12 with the vibrations being attenuated during the
transmission of the elastic waves.
Further, the torsion of the racket frame generated by the out-of-plane
component of the tensile force of the strings 13 has the action of
restraining the resonance of the racket frame. In this manner, the
restrained vibrations of the strings 13 are transmitted to the grip
portion 12.
Tennis rackets shown in the comparison examples of FIGS. 4 through 8 (first
through fifth comparison) were prepared as conventional tennis rackets to
compare the repulsion performance and rigidity of the tennis racket
according to the present invention with that of the conventional tennis
rackets. The size of each portion of each tennis racket is shown in Table
1.
The entire length (L) and thickness (m) of the wall of the
string-installing portion of each of the comparison tennis rackets were
equal to those of the tennis rackets according to the first and second
embodiments.
As apparent from the sizes shown in Table 1, the thicknesses of the first
three comparison tennis rackets were equal to each other, whereas the
ball-hitting areas thereof were differentiated from each other. That is,
the ball-hitting area of the second comparison tennis racket was set to be
greater than that of the first comparison tennis racket, and that of the
third comparison tennis racket was greater than that of the second
comparison tennis racket. The first and second comparison tennis rackets
were mid (standard) size, whereas the third comparison tennis racket was
the large racket with a standard thickness. The fourth and fifth
comparison tennis rackets were thick rackets. The fifth comparison racket
was not only a thick racket but also a large racket, i.e., had a large
ball-hitting area.
Tests for examining the repulsion performance of the tennis rackets
according to the first and second embodiments and that of the first
through fifth comparison tennis rackets were conducted.
In the test, a ball 30 was thrown to each tennis racket having strings 13
installed thereon, and a ball speed V1 colliding with the ball-hitting
surface and a ball speed V2 reflected thereby were measured. Further, the
restitution coefficients V2/V1 were calculated.
The results are as shown in Table 1 and FIG. 10 and the following (a)
through (c) were confirmed.
TABLE 2
______________________________________
Rigidity [kg/cm]
Restitution Top Side Plain
coefficient pressure pressure pressure
______________________________________
E1 0.424 87 61 42
E2 0.437 123 95 35
C1 0.391 97 75 39
C2 0.407 83 67 43
C3 0.425 73 50 35
C4 0.414 84 59 54
C5 0.441 68 55 47
______________________________________
In the above, E1 and E2 indicate the tennis rackets according to the first
embodiment and the second embodiment, respectively; C1 through C5 indicate
a first comparison tennis racket through a fifth comparison tennis racket,
respectively.
(a) In the first through third comparison tennis rackets with a standard
thickness size (thickness (h)=20.21 mm), the restitution coefficient
became larger with (the) an increase in the ball hitting area thereof.
Therefore, the advantage of a "large racket" was confirmed.
(b) The restitution coefficients of the fourth and fifth comparison thick
rackets were greater than those of the first through third comparison
tennis rackets in standard thickness. That is, the advantage of a "thick
racket" was confirmed. The restitution coefficient of ball-hitting area
(large racket) was greater than that of the fourth comparison tennis
racket. Therefore, the fifth comparison tennis racket had the advantage of
the large racket as well.
(c) Although the tennis racket according to the first embodiment had a
standard thickness (thickness h=21 mm, the length b1 of projection=6 mm),
the spring effect of the torsion brought about by the twisted projection
20 of the string-installing portion 10 allowed the tennis racket,
according to the first embodiment, to have its restitution coefficient as
high as that of the thick racket.
The tennis racket according to the second embodiment (b1=10 mm) having a
longer projection 20 had a restitution coefficient as high as that of the
fifth comparison tennis racket having the advantage of the large racket as
well as that of the thick racket.
Rigidity to top pressure, rigidity to side pressure, and rigidity to plane
pressure were tested on the tennis rackets according to the first and
second embodiments and the first through fifth comparison tennis rackets.
In the top pressure rigidity test, a downward load was applied to the top
portion of each racket by a pressure applying tool 32, with both the lower
positions of the string-installing portion 10 (namely, the position
between the side portion and yoke portion) being fixed by supporting tools
31 to support each racket vertically, as shown in FIG. 11A, so as to find
a spring constant (rigidity) kgf/cm for each racket based on the flexure
amount of the racket frame. The top pressure rigidity is an index for
comparing the in-plane rigidities of the rackets with respect to each
other.
The test for examining the side pressure rigidity was conducted as follows.
A load was applied to one side frame by the pressure applying tool 32,
with the other side frame being supported on a fixing base 33, as shown in
FIG. 11B. The side pressure rigidity is an index for comparing the
in-plane rigidities of the rackets with each other.
The test for examining the plane pressure rigidity was conducted as
follows. A load was applied in the downward direction to the center of a
racket frame horizontally placed, between the top of the racket frame and
the grip end as shown in FIG. 11C, with both a point in the vicinity of
the top of the racket frame and a point in the vicinity of the grip end
being supported by a supporting tools 34. The plane pressure rigidity
indicates an index for comparing the out-of-plane rigidities of the
rackets with respect to each other.
The result of the plane pressure rigidity test is as shown in Table 2. The
relationship between the ball-hitting area of each racket and the measured
value of the plane pressure rigidity is as shown in FIG. 12.
As apparent from Table 2 and FIG. 12, the thickness (h) of the
string-installing portion is 21 mm in the tennis rackets according to the
first and second embodiments, whereas that of the string-installing
portion is 20.21 mm in the first through third comparison tennis rackets.
Therefore, the plane pressure rigidities of the former are in almost the
same level as those of the latter.
It was confirmed that the fourth and fifth comparison, thick rackets having
a thickness (h) of 30 mm were higher in plane pressure rigidity than
tennis rackets according to the first and second embodiments having a
standard thickness and the first through third comparison tennis rackets
having a standard thickness as well.
It was analogized that all of the first through third comparison tennis
rackets having the standard thickness and the fourth and fifth comparison
thick rackets became lower in plane pressure rigidity with an increase in
the ball-hitting area thereof, but the level of the plane pressure
rigidity of the former was not much different from that of the latter
although the thickness (h) of the former and that of the latter were much
different from each other. That is, the difference in the plane pressure
rigidity was not much for the difference in the thickness (h).
It can be said from the above description that the tennis rackets according
to the first and second embodiments, having a standard thickness, give a
soft ball-hitting feeling to the player because the racket frames are
flexible, which makes the time period of the contact between the ball and
the strings long. Accordingly, the tennis rackets having a standard
thickness according to the first and second embodiments is capable of
controlling the ball more easily than the thick racket.
The results of the measurements of the top pressure rigidities are shown in
Table 2. The relationship between the top pressure rigidities and the
ball-hitting area is shown in FIG. 13.
As shown in Table 2 and FIG. 13, in the first through fifth comparison
tennis rackets, the top pressure rigidity dropped with an increase in the
ball-hitting area, irrespective of the thickness (h) thereof. This means
that with an increase in the ball-hitting area, the in-plane rigidity of
each tennis racket decreases and thus the racket frame is deformed in a
large degree and thus the ball control performance thereof becomes
unfavorable when the ball is hit thereby.
Each of the tennis rackets according to the first and second embodiments
had a top pressure rigidity much higher than that of conventional tennis
rackets in which the string-installing portion is not T-shaped in cross
section and the ball-hitting area (100 square inches) is equal to that of
each of the rackets according to the first and second embodiments. That
is, the in-plane rigidity of each of the tennis rackets according to the
first and second embodiments is higher than that of conventional tennis
rackets, indicated as the first through fifth comparison tennis rackets.
The result is due to the reasons given as to why the string-installing
portion is T-shaped in cross section and the state in which the projection
20 mounted on the inner surface of the base 21 serves as a generated hoop.
In this manner, the effect of the hoop for suppressing the occurrence of
in-plane deformation is generated to improve the stability of the
ball-hitting surface.
The results of the measurements of the side pressure rigidities are shown
in Table 2. The relationship between the side pressure rigidities and the
ball-hitting area is shown in FIG. 14.
As shown in Table 2 and FIG. 14, the tennis rackets according to the first
and second embodiments were higher than the first through fifth comparison
tennis rackets in the side pressure rigidity thereof.
The test results indicate that the tennis rackets according to the first
and second embodiments can be made to be higher than the first through
fifth comparison tennis rackets in the in-plane rigidity thereof and that
the in-plane rigidity can be freely set by altering the length of the
projection 20 of the string-installing portion 10.
Further, the test results also indicate that in the racket according to the
present invention, even though the ball-hitting area is set to be great to
provide the advantage of the large racket, the ball control performance
can be improved by setting the in-plane rigidity to be high.
From the above-described test results of repulsion performance and
rigidity, the following points were confirmed.
The T-shaped string-installing portion allows the repulsion performance of
the racket to be improved due to the spring effect of the torsion which
brought about the twisted projection 20.
The construction of the racket according to the present invention which
comprises the T-shaped string-installing portion, overcomes the
disadvantage of a conventional large racket having a large ball-hitting
area or a conventional thick racket having a thick string-installing
portion. That is, a "large racket" according to the present invention
comprising a T-shaped string-installing portion and a large ball-hitting
surface or a "thick racket" according to the present invention, comprises
a thick string-installing portion have a favorable ball control
performance and gives a soft ball-hitting feeling to the player similarly
to the mid size racket in addition to a favorable repulsion performance
which is a feature of the large or thick racket. That is, the present
invention provides a large racket or a thick racket superior in
ball-hitting feeling and ball control performance, and repulsion
performance.
In order to check the test result, tennis balls were hit by the tennis
rackets according to the first and second embodiments and the first
through fifth comparison tennis rackets.
Ten persons hit tennis balls by the tennis rackets according to the first
and second embodiments and the first through fifth comparison tennis
rackets in order to test the performance thereof.
The test results are as follows:
Regarding the repulsion performance, eight persons out of 10 responded that
"The repulsion performances of the rackets according to the first and
second embodiments were equivalent to that of the large third comparison
racket and that of thick fifth comparison racket. The repulsion
performance of the racket according to the second embodiment was superior
to that of the racket according to the first embodiment."
Regarding the ball control performance, seven persons out of 10 responded
that "The ball control performances of the rackets according to the first
and second embodiments were equivalent to those of the first and second
comparison rackets. The ball control performances of the third and fifth
comparison rackets were less favorable than those of the rackets according
to the first and second embodiments and the first and second comparison
rackets. The ball control performances of the rackets according to the
first and second embodiments were not different from each other".
Regarding ball-hitting feeling, 10 persons responded that "The feeling
given by the rackets according to the first and second embodiments was
equivalent to that given by the first, second, and third comparison
rackets and softer than that given by the fourth and fifty comparison
rackets".
Regarding string vibration-restraining effect of the string-installing
portion, six persons responded that "The string-installing portion was
effective for restraining the vibration of strings." Four persons
responded that "The string-installing portion was ineffective for
restraining the vibration of strings."
As apparent from the foregoing description, according to the tennis racket
of the present invention, the string-installing section having a T-shaped
cross section allows a novel spring of torsion deformation to be generated
when a tennis ball is hit, and the novel spring improves the repulsion
performance of the tennis racket.
Accordingly, the repulsion performance of a mid (standard) size racket is
as high as that of a large or thick racket although the ball-hitting area
of the mid size racket is not as great as the large racket and the
thickness thereof is not as great as that of the thick racket.
Because the string-installing portion is T-shaped in cross section, the
in-plane rigidity can be freely designed and thus a high in-plane rigidity
can be maintained even though the ball-hitting area is set to be large.
The "Hoop effect" can be generated unlike the conventional racket, thus
dramatically improving the in-plane stability. Therefore, the large
racket, having a great ball-hitting area, developed to increase repulsion
performance, is allowed to have a favorable ball control performance.
Further, the vibration of the strings can be restrained in hitting a ball
and thus a player has a favorable ball-hitting feeling.
Although the present invention has been fully described in connection with
the preferred embodiments thereof with reference to the accompanying
drawings, it is to be noted that various changes and modifications are
apparent to those skilled in the art. Such changes and modifications are
to be understood as included within the scope of the present invention as
defined by the appended claims unless they depart therefrom.
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